details

property	value
status	complete
benchmark	#4.29.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n070.star.cs.uiowa.edu
space	Strategy_removed_AG01

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	1.76551 seconds
cpu usage	5.59773
user time	4.52644
system time	1.07129
max virtual memory	5694460.0
max residence set size	79012.0

stage attributes

key	value
starexec-result	YES

output

YES Problem: even(0()) -> true() even(s(0())) -> false() even(s(s(x))) -> even(x) half(0()) -> 0() half(s(s(x))) -> s(half(x)) plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) times(0(),y) -> 0() times(s(x),y) -> if_times(even(s(x)),s(x),y) if_times(true(),s(x),y) -> plus(times(half(s(x)),y),times(half(s(x)),y)) if_times(false(),s(x),y) -> plus(y,times(x,y)) Proof: DP Processor: DPs: even#(s(s(x))) -> even#(x) half#(s(s(x))) -> half#(x) plus#(s(x),y) -> plus#(x,y) times#(s(x),y) -> even#(s(x)) times#(s(x),y) -> if_times#(even(s(x)),s(x),y) if_times#(true(),s(x),y) -> half#(s(x)) if_times#(true(),s(x),y) -> times#(half(s(x)),y) if_times#(true(),s(x),y) -> plus#(times(half(s(x)),y),times(half(s(x)),y)) if_times#(false(),s(x),y) -> times#(x,y) if_times#(false(),s(x),y) -> plus#(y,times(x,y)) TRS: even(0()) -> true() even(s(0())) -> false() even(s(s(x))) -> even(x) half(0()) -> 0() half(s(s(x))) -> s(half(x)) plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) times(0(),y) -> 0() times(s(x),y) -> if_times(even(s(x)),s(x),y) if_times(true(),s(x),y) -> plus(times(half(s(x)),y),times(half(s(x)),y)) if_times(false(),s(x),y) -> plus(y,times(x,y)) TDG Processor: DPs: even#(s(s(x))) -> even#(x) half#(s(s(x))) -> half#(x) plus#(s(x),y) -> plus#(x,y) times#(s(x),y) -> even#(s(x)) times#(s(x),y) -> if_times#(even(s(x)),s(x),y) if_times#(true(),s(x),y) -> half#(s(x)) if_times#(true(),s(x),y) -> times#(half(s(x)),y) if_times#(true(),s(x),y) -> plus#(times(half(s(x)),y),times(half(s(x)),y)) if_times#(false(),s(x),y) -> times#(x,y) if_times#(false(),s(x),y) -> plus#(y,times(x,y)) TRS: even(0()) -> true() even(s(0())) -> false() even(s(s(x))) -> even(x) half(0()) -> 0() half(s(s(x))) -> s(half(x)) plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) times(0(),y) -> 0() times(s(x),y) -> if_times(even(s(x)),s(x),y) if_times(true(),s(x),y) -> plus(times(half(s(x)),y),times(half(s(x)),y)) if_times(false(),s(x),y) -> plus(y,times(x,y)) graph: if_times#(false(),s(x),y) -> times#(x,y) -> times#(s(x),y) -> if_times#(even(s(x)),s(x),y) if_times#(false(),s(x),y) -> times#(x,y) -> times#(s(x),y) -> even#(s(x)) if_times#(false(),s(x),y) -> plus#(y,times(x,y)) -> plus#(s(x),y) -> plus#(x,y) if_times#(true(),s(x),y) -> times#(half(s(x)),y) -> times#(s(x),y) -> if_times#(even(s(x)),s(x),y) if_times#(true(),s(x),y) -> times#(half(s(x)),y) -> times#(s(x),y) -> even#(s(x)) if_times#(true(),s(x),y) -> plus#(times(half(s(x)),y),times(half(s(x)),y)) -> plus#(s(x),y) -> plus#(x,y) if_times#(true(),s(x),y) -> half#(s(x)) -> half#(s(s(x))) -> half#(x) times#(s(x),y) -> if_times#(even(s(x)),s(x),y) -> if_times#(false(),s(x),y) -> plus#(y,times(x,y)) times#(s(x),y) -> if_times#(even(s(x)),s(x),y) -> if_times#(false(),s(x),y) -> times#(x,y) times#(s(x),y) -> if_times#(even(s(x)),s(x),y) -> if_times#(true(),s(x),y) -> plus#(times(half(s(x)),y),times(half(s(x)),y)) times#(s(x),y) -> if_times#(even(s(x)),s(x),y) -> if_times#(true(),s(x),y) -> times#(half(s(x)),y) times#(s(x),y) -> if_times#(even(s(x)),s(x),y) -> if_times#(true(),s(x),y) -> half#(s(x)) times#(s(x),y) -> even#(s(x)) -> even#(s(s(x))) -> even#(x) plus#(s(x),y) -> plus#(x,y) -> plus#(s(x),y) -> plus#(x,y) half#(s(s(x))) -> half#(x) -> half#(s(s(x))) -> half#(x) even#(s(s(x))) -> even#(x) -> even#(s(s(x))) -> even#(x) SCC Processor: #sccs: 4 #rules: 6 #arcs: 16/100 DPs: if_times#(false(),s(x),y) -> times#(x,y) times#(s(x),y) -> if_times#(even(s(x)),s(x),y) popout

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